8.5.B
The Standard
represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify a constant rate and a starting value that is not zero. They show the same situation with a table, plotted points, a line, and an equation.
What Mastery Looks Like
- Students correctly identify the constant rate and nonzero starting value from any representation. They create a table, graph, and equation that show the same relationship and explain how the slope and intercept appear in each.
Common Misconceptions
- Students may treat the starting value as zero or confuse it with the rate of change. They may switch the slope and y-intercept or plot the intercept on the x-axis.
How to Assess It
- Give this exit ticket: “A tank starts with 12 gallons and fills 3 gallons per minute. Make a table, graph the first four points, and write an equation.”
Lesson moves
Ways to Teach It
Give pairs cups and counters to model a starting amount plus equal additions, then record totals in a table and graph them.
Ask students to explain in writing where the starting value and rate appear in a table, graph, and equation.
Run a matching game with cards showing equations, tables, graphs, slopes, and starting values from the same relationships.
Compare a taxi fare with a base fee and per-mile charge, then represent the cost with a table, graph, and equation.
Keep exploring
Related Standards
- 8.5.F
distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0
- 6.6.C
represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b
- 8.5.A
represent linear proportional situations with tables, graphs, and equations in the form of y = kx
- 8.5.I
write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations
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